Topological Floquet engineering using two frequencies in two dimensions

TL;DR

This paper investigates two-frequency Floquet driving in two-dimensional lattice models, revealing new topological phases, symmetry-breaking effects, and potential applications in ultracold atoms and nonlinear Hall phenomena.

Contribution

It extends Floquet engineering methodology to two dimensions, demonstrating competing topological phases and tunable symmetry breaking via two-tone drives.

Findings

Identification of competing topological phases in 2D lattices.

Demonstration of independent tuning of inversion and time-reversal symmetry breaking.

Potential for generating topological bands in ultracold atom systems.

Abstract

Using two-frequency driving in two dimensions opens up new possibilites for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyse the resulting effective Floquet bandstructures both numerically and analytically. On the one hand, we extend the methodology of Sandholzer et al. [10.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topological phases in a simple Bravais lattice when the two resonant drives at $1\omega$ and $2\omega$ interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topological bands for ultracold atoms, and the realisation of non-linear Hall effects as well as Haldane's parity anomaly in inversion-symmetric parent lattices.